In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.
@article{bwmeta1.element.doi-10_1515_math-2016-0012,
author = {Abedallah Rababah},
title = {The best uniform quadratic approximation of circular arcs with high accuracy},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {118-127},
zbl = {1347.41008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0012}
}
Abedallah Rababah. The best uniform quadratic approximation of circular arcs with high accuracy. Open Mathematics, Tome 14 (2016) pp. 118-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0012/